A Treatise on Mensuration for the Use of Schools (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1837 Excerpt: ...of one being 14 and 12 inches, and the corresponding dimensions of the other 6 and 4 inches;. also the length 30 feet? 14 12 12 X 14 = 168 6 4 6 X 4 = 24----20 X 16 = 320 20 16 512 square inches =--square teet. 32 2 Then i X'--X 30 = 18--feet, the solidity. 6. How many solid inches in a mahogany plank, the length and breadth of one end being 81-and 55 inches, the length and breadth of the other end 41 and 29 inches, and the length of the plank 47 inches? Ans. 126340-59375 cubic inches. PROBLEM III. Given the breadth of a rectangular plank in inches, to find how much in length will make a foot, or any other required quantity. Rule. Divide 144, or the area to be cut off, by the breadth in inches, and the quotient will be the length in inches. This rule is correct, being that given for finding the solidity of lhe prismaid--which see. Let B and b be the breadths of the two ends, D and d the depths, and L the length;(BD + (B + 4)x (D + d) +bd) X L = the true solidity, as in the rule for the prismoid. The Carpenters' rule is furnished with a scale which answers the purpose of this rule. It is called a table of board measure, and is in the following form: If the breadth be 1 inch, the length standing against it is 12 feet; if the breadth be 2 inches, the length standing against it is 6 feet; if the breadth be 5 inches, the length is 2 feet 5 inches, &c. When the breadth goes beyond the limits of the table on the rule, it must be shut, and then you are to look for the breadth in the line of board measure, which runs along the rule from the table of board measure, and over against it on the opposite side, in the scale of inches, will be found the length required. For example, if the breadth be 9 inches, you will find the length against it to be 16 inches; ...